Re-Redesigned: Darren Kuropatwa and Dan Meyer

So Dan Meyer took an original slide of Darren Kuropatwa’s and redesigned it.

Darren’s slide:

Dan’s slide:

Now, this is by any measure better, not only for a more striking and relevant use of visuals, but forcing students to decide on using the mean themselves and realizing through their own calculations the two means are equal.

Dan finishes the lesson with a discussion of (statistical) range, which for the above example is enough to settle the matter. I feel vaguely unsatisfied with that, simply because “subtract the highest element from the lowest” is a concept my students take about 10 seconds to grasp. What could have been a complex mathematical framework veers into something almost too easy to teach (and seems to exist solely to confuse students when they encounter the other type of mathematical range).

So, how could one take this further?

Lower level mathematics:

(I made the numbers up because I do not have Dan’s original choice of route, but one could get the real estimates off Google Maps.)

Notice how when adding up the numbers it appears the blue route is faster. Why the inconsistency? (While I made this one up, I find it a realistic reflection of my own experience with map estimates.) This can also lead to a discussion of map scale and estimates of average velocity on each street as well as average velocity for the entire route.

True ambition could lead to a geometry lesson as students figure out arc length to get at the curved streets.

Upper level mathematics:

Now the statistical ranges are equal: what metric can we use to say the green route is superior? This can lead nicely into standard deviation; I wouldn’t give the formula at all at first, but have students make various attempts at expressing the variation mathematically on their own.